Flashcards — Chapter 11 🃏

Angular Momentum and Rotational Dynamics — conservation laws and what they unleash! ⚙️

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📋 Card sets: key terms and formulas

Section §11.1 — Angular Momentum

1. Angular momentum (definition) — L = Iω (kg·m²/s); measure of an object's spin
2. Angular momentum for a single particle — \vec L = \vec r × \vec p = m\vec r × \vec v (cross product of position and linear momentum)
3. Units of angular momentum — kg·m²/s or J·s (energy × time)
4. Angular momentum relative to reference — depends on choice of rotation axis
5. Angular velocity from angular momentum — for a fixed axis, ω = L/I

Section §11.2 — The Torque-Angular Momentum Relation

6. Equation of motion (rotational) — dL/dt = Στ (rate of change of angular momentum = net torque)
7. Newton's second law (angular momentum form) — external torque changes angular momentum
8. Without external torque — if τ_ext = 0, then dL/dt = 0 and L is constant
9. Impulse-momentum for rotation — Δτ·Δt = ΔL (torque impulse = change in angular momentum)

Section §11.3 — Conservation of Angular Momentum

10. Conservation law for angular momentum — if net external torque is zero, total angular momentum is constant: L_initial = L_final
11. Isolated system — no external forces (or only central forces), angular momentum is conserved
12. Figure skater example — skater pulls arms in; I decreases; ω increases (because L is conserved)
13. Skater's final angular velocity — ω_final = L/I_final = (I_initial·ω_initial) / I_final
14. Planetary motion — planets maintain constant L as they orbit; closer to Sun → faster orbit
15. Collision and sticking (rotating) — two rotating masses collide and stick; angular momentum is conserved

Section §11.4 — Spin and Orbital Angular Momentum

16. Spin angular momentum — intrinsic rotation of an object about its own axis
17. Orbital angular momentum — motion about an external center (e.g., planet orbiting the Sun)
18. Total angular momentum — L_total = L_spin + L_orbital (vector sum of the two)
19. Electron in an atom — has both spin L_s (intrinsic) and orbital L_l (around nucleus)
20. Coupling of spin and orbital — in atoms, L_s and L_l couple to form total L_j

Section §11.5 — Gyroscopes and Precession

21. Gyroscope — a rapidly spinning object under external torque
22. Naive expectation — if torque is applied, the object should tilt in that direction (fall)
23. Precession — instead, the angular momentum vector changes direction gradually (not instantly)
24. Precession rate — Ω = τ/L (torque / angular momentum = rate of direction change)
25. Stable gyroscope — high-speed spinning wheel with large L; Ω is small; nearly stationary
26. Gyroscope in practice — bicycle wheel, motorcycle wheel, gyroscopic compass in aircraft, stabilization of space probes

Section §11.6 — Collision and Sticking Systems

27. Inelastic collision (rotational) — two rotating objects collide and stick together; angular momentum is conserved
28. Final angular velocity — I₁ω₁ + I₂ω₂ = (I₁ + I₂)ω_final (from conservation)
29. Energy in rotational collision — unlike angular momentum, rotational kinetic energy is not conserved; some is lost
30. Disk-on-disk collision — spinning disk lands on stationary disk; friction causes them to stick; final ω by conservation

Section §11.7 — Equilibrium and Stability

31. Rotational equilibrium (first condition) — ΣF = 0 (no net force)
32. Rotational equilibrium (second condition) — Στ = 0 (no net torque)
33. Static equilibrium — both conditions hold (no linear or rotational motion)
34. Dynamic equilibrium — net force and net torque are zero, but the object may be moving

Section §11.8 — Natural Applications

35. Planets and Kepler's second law — equal areas in equal times ⟺ conservation of orbital angular momentum
36. Black holes — spin angular momentum (mass in rotation) characterizes their properties
37. Astrolabe and star-finding — high-speed gyroscope nearly stationary in space; used for navigation
38. Coriolis effect — in a rotating frame (e.g., Earth), objects appear to deviate from straight paths
39. Black hole and stellar tidal forces — orbital angular momentum determines closest approach

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📊 Topics covered

• Angular momentum — definition, units, calculation
• Torque-angular momentum relation — equation of motion
• Conservation of angular momentum — when and why
• Spin and orbital — distinction and combination
• Gyroscope and precession — 3D dynamics
• Collision systems — inelastic, rotational
• Natural applications — planets, astrolabe, black holes, navigation

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What comes next:

👉 §11.1–§11.3 — worked problems (step-by-step examples)
👉 §11.4–§11.6 — practice problems (exercises)
👉 §11.7–§11.8 — Q&A (answers to common misconceptions)

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